Tournament

Problem Description

There are $n$ players in a competition, with ability values $a_1, a_2, \dots, a_n$.

A total of $n - 1$ rounds are held. In each round, among the players still remaining, any two players $i, j$ are chosen. If $|a_i - a_j| > K$, then the player with the higher ability value wins and the player with the lower ability value is eliminated. If $|a_i - a_j| \le K$, then either of the two players may win and the other is eliminated.

After $n - 1$ rounds, only one player remains. How many players could possibly be the final winner?

Input Format

The first line contains two integers $n, K$, the total number of players and the parameter of the winning condition.

The next line contains $n$ integers $a_1, a_2, \dots, a_n$, the ability values of the players.

Output Format

Output one integer: the number of players that could possibly win in the end.

Sample Input

5 3
1 5 9 6 3

Sample Output

5

Constraints

There are $10$ test cases in total.

Test point $1$: $n \leq 5$.

Test point $2$: $n \leq 10$.

Test points $3, 4, 5$: $n \leq 1000$.

For $100\%$ of the data: $n \leq 10^5$, $1 \leq a_i, K \leq 10^9$.

Hint

See the accompanying problem materials.